Related papers: 8-Vertex Correlation Functions and Twist Covarianc…
In this paper, we construct various simple vertex superalgebras which are extensions of affine vertex algebras, by using abelian cocycle twists of representation categories of quantum groups. This solves the Creutzig and Gaiotto conjectures…
We find some exact solutions of the Knizhnik-Zamolodchikov equation for the four point correlation functions that occur in the SL(2,R) WZNW model. They exhibit logarithmic behaviour in both the Kac-Moody and Virasoro parts. We discuss their…
Cherednik's quantum affine Knizhnik-Zamolodchikov equations associated to an affine Hecke algebra module M form a holonomic system of q-difference equations acting on M-valued functions on a complex torus T. In this paper the quantum affine…
We prove in this paper that the elliptic $R$--matrix of the eight vertex free fermion model is the intertwiner $R$--matrix of a quantum deformed Clifford--Hopf algebra. This algebra is constructed by affinization of a quantum Hopf…
$q$-vertex operators for quantum affine algebras have played important role in the theory of solvable lattice models and the quantum Knizhnik-Zamolodchikov equation. Explicit constructions of these vertex operators for most level one…
We prove that the logarithm of a group-like element in a free algebra coincides with its image by a certain linear map. We use this result and the formula of Le and Murakami for the Knizhnik-Zamolodchikov (KZ) associator $\Phi$ to derive a…
We pursue our study of generalised Kac-Moody and Virasoro algebras defined on compact homogeneous manifolds. Extending the well-known Vertex operator in the case of the two-torus or the two-sphere, we obtain explicit bosonic realisations of…
This paper is to study what we call twisted regular representations for vertex operator algebras. Let $V$ be a vertex operator algebra, let $\sigma_1,\sigma_2$ be commuting finite-order automorphisms of $V$ and let…
We formulate the basic properties of q-vertex operators in the context of the Andrews-Baxter-Forrester (ABF) series, as an example of face-interaction models, derive the q-difference equations satisfied by their correlation functions, and…
The search for elliptic quantum groups leads to a modified quantum Yang-Baxter relation and to a special class of quasi-triangular quasi Hopf algebras. This paper calculates deformations of standard quantum groups (with or without spectral…
This paper is a continuation of "Quantization of Lie bialgebras, III" (q-alg/9610030, revised version). In QLB-III, we introduced the Hopf algebra F(R)_\z associated to a quantum R-matrix R(z) with a spectral parameter, and a set of points…
Introducing an H-Hopf algebroid structure into U_{q,p}(\widedhat{sl}_2), we investigate the vertex operators of the elliptic quantum group U_{q,p}(\widedhat{sl}_2) defined as intertwining operators of infinite dimensional…
We obtain the operator algebra of each twisted sector of all WZW orbifolds, including the general twisted current algebra and the algebra of the twisted currents with the twisted affine primary fields. Surprisingly, the twisted right and…
We introduce the quasi-Hopf superalgebras which are $Z_2$ graded versions of Drinfeld's quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the…
Topological quantum field theory (TQFT) is a powerful tool to describe homologies, which normally involve complexes and a variety of maps/morphisms, what makes a functional integration approach with a sum over a single kind of maps…
One purpose of this paper is to construct twisted q-Euler numbers by using p-adic invariant integral on Zp in the sense of fermionic. Finally, we consider twisted Euler q-zeta function and q-l-series which interpolate twisted q-Euler…
We derive the exchange relations of the vertex operators of $U_q(A_2^{(2)})$ and show that these vertex operators give the bosonization of the Izergin-Korepin model. We give an integral expression of the correlation functions of the…
We quantize the $SU(n)$ Wess-Zumino-Witten model in terms of left and right chiral variables choosing an appropriate gauge and we compare our results with the results that have been previously obtained in the algebraic treatment of the…
An explicit construction for Q-operators of the finite XXZ spin-chain with twisted boundary conditions is presented. The massless and the massive regime is considered as well as the root of unity case. It is explained how these results…
In this paper, we present a geometric description of foams, which are prevalent in topological quantum field theories (TQFTs) based on quantum algebra, and reciprocally explore the geometry of Rozansky-Witten (RW) theory from an algebraic…